Efficient simulation of slightly entangled, forced, synthetic quantum matter.

Tensor lattices are classes of ansätze that offer efficient parameterization of wave functions of many-body quantum systems with local Hamiltonians. Famous examples of these classes are the matrix product states (MPS) [Fannes92, White92]. Applications of tensor networks range from emerging phenomena in statistical mechanics and quantum matter, to ideas in quantum gravity and neural networks. Tensor networks have been very successful characterizing the ground state and excitations of partially entangled systems in the discrete (lattice). Adapting their success to the efficient description of the ground state of continuous quantum systems is an intriguing avenue of research. Continuous tensor lattices are nonperturbative ansätze for the analysis of quantum field theories. In fact, continuum MPS (cMPS) were recently proposed to study the ground state of quantum field theories in 1 + 1 dimensions [Verstraete10]. Using cMPS, together with international collaborators, we built a bosonic model in the continuum that exhibits a phase transition. super-fluid/quasi-crystal quantum[Rincón15]. This compares to the celebrated Lieb-Liniger model (the most basic correlated model on the continuum) where only superfluidity is present. Our model shows a quantum phase transition in the simplest continuous configuration. From the point of view of conformal field theory, our model has a central unit charge with a radius of compactification at (0, ¥), which contrasts with Lieb-Liniger, where said radius is at [1, ¥).